We study the relations between stellar mass , star formation history , size and internal structure for a complete sample of 122,808 galaxies drawn from the Sloan Digital Sky Survey .
We show that low-redshift galaxies divide into two distinct families at a stellar mass of 3 \times 10 ^ { 10 } M _ { \odot } .
Lower mass galaxies have young stellar populations , low surface mass densities , and the low concentrations typical of disks .
Their star formation histories are more strongly correlated with surface mass density than with stellar mass .
A significant fraction of the lowest mass galaxies in our sample have experienced recent starbursts .
At given stellar mass , the sizes of low mass galaxies are log-normally distributed with dispersion \sigma ( \ln R _ { 50 } ) \sim 0.5 , in excellent agreement with the idea that they form with little angular momentum loss through cooling and condensation in a gravitationally dominant dark matter halo .
Their median stellar surface mass density scales with stellar mass as \mu _ { * } \propto M _ { * } ^ { 0.54 } , suggesting that the stellar mass of a disk galaxy is proportional to the three halves power of its halo mass .
All this suggests that the efficiency of the conversion of baryons into stars in low mass galaxies increases in proportion to halo mass , perhaps as a result of supernova feedback processes .
At stellar masses above 3 \times 10 ^ { 10 } M _ { \odot } , there is a rapidly increasing fraction of galaxies with old stellar populations , high surface mass densities and the high concentrations typical of bulges .
In this regime , the size distribution remains log-normal , but its dispersion decreases rapidly with increasing mass and the median stellar mass surface density is approximately constant .
This suggests that the star formation efficiency decreases in the highest mass halos , and that little star formation occurs in massive galaxies after they have assembled .